Properties of Normal Curves

Normal Distribution Curves are symmetrical bell-shaped curves possessed of distinct characteristics.  For example, the area under any given normal curve has the same proportional distribution to its total area; that is to say, the area from negative infinity to one S away from the mean is always the same: 84.13 percent (0.8413).  The total area under a normal curve is always equal to one.  Additionally, the curves never quite reach Y=0; curve extends to infinity and negative infinity.

The first Illustration shows a few normal curves with equal means, but unequal standard deviations.  The tall and skinny graph has a lesser S value than the others, and a greater frequency of values closer to the Mean.

The second Illustration depicts curves with equivalent means and standard deviations, but unequal population sizes.

As you can see, the shape that a Normal Curve takes is dependent upon its mean and standard deviation, and though it always has the properties listed above, the possibilities as to the shape that the curve may take are infinite.

One particularly important Normal Curve is the Standard Normal Distribution.